"It's not something we can be concerned about," Rooney told reporters when asked about Allardyce's sacking last week after one game in charge following a newspaper sting.
"As a group we need to stick together and concentrate on the football and I am sure there will be no problem doing that. The other side is not our issue," Rooney added.
"I'm sure it's been a tough couple of weeks for the FA but the players have concentrated on club football and we have to focus on the games and training."
When pressed for his thoughts on Allardyce, Rooney said: "It's a shame. I think everyone could see how excited Sam was for the job and he showed that to the players. I am sure he deeply regrets it but that was a decision for the FA to take."
Gareth Southgate has been put in charge for the next four games, including Saturday's home match against Malta and the away game against Slovenia on Tuesday.
Southgate, like Allardyce, has said that Rooney will continue as captain, describing him as the "outstanding leader in the group" despite him losing his place in the Manchester United starting team.
Rooney returned the compliment.
"He's done a very good job with the Under-21s, he's worked with a lot of the players and he's been given the opportunity to show what he can do at senior level," he said of his new boss.
"We have to buy into his ways and try to take his ideas on board and put them into action on the pitch.
"I'm not sure if it's starting again, we need to build on the three points in the last game," he added of the 1-0 win in Slovakia in Allardyce's sole match last month.
Rooney, who once again looked as if he would rather be anywhere in the world than sitting at a podium facing the media, was clearly unimpressed about being asked what position he might take having bounced from forward to midfield in recent months.
"It's getting a bit tired the questions about where I'm going to play," he said.
"I've answered it many times and it's the same answer – I play where the manager wants me to play – I don't pick myself."
(Editing by Ed Osmond)
